determinant

sum of signed terms of n factors from n×n matrix with no two factors sharing row or column
rdfs:label
"determinant"@en
skos:altLabel
"determinant of a square matrix"@en
"determinant of matrix"@en
"matrix determinant"@en
schema:description
"sum of signed terms of n factors from n×n matrix with no two factors sharing row or column"@en
schema:dateModified "2026-09-20T09:19:33+00:00"^^xsd:dateTime
schema:version 2547901977
wikibase:identifiers 43
wikibase:sitelinks 78
wikibase:statements 78
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p:direct-normalized/P227 <https://d-nb.info/gnd/4138983-9>
p:direct-normalized/P2347 <http://www.yso.fi/onto/yso/p11285>
p:direct-normalized/P244 <http://id.loc.gov/authorities/names/sh85037299>
p:direct-normalized/P268 <http://data.bnf.fr/ark:/12148/cb11975737s#about>
p:direct-normalized/P349 <http://id.ndl.go.jp/auth/ndlna/00562696>
p:direct-normalized/P508 <http://purl.org/bncf/tid/32649>
p:direct-normalized/P6366 <https://makg.org/entity/158041659>
<https://makg.org/entity/2778383128>
p:direct-normalized/P7033 <http://vocabulary.curriculum.edu.au/scot/15495>
wdt:P10017 "determinante"
wdt:P1036 "512.9432"
wdt:P10376 "mathematics/det"
wdt:P1051 "7275"
wdt:P11497 "1.2.E58"
"1.3.i"
wdt:P12385 "algebra-multilineal"
wdt:P12457 matrix transposition
change of basis
wdt:P12888 "df-mdet"
wdt:P1296 "0267697"
wdt:P13204 "bs92fr9d"
wdt:P1343 ISO 80000-2:2019 Quantities and units — Part 2: Mathematics
Mathwords
Small Brockhaus and Efron Encyclopedic Dictionary
New Encyclopedic Dictionary
mathisfun.com
mathisfun.com dictionary
Brockhaus and Efron Encyclopedic Dictionary
Encyclopædia Britannica 11th edition
wdt:P13591 "concept/03e46d8a-03af-46eb-8020-54fe63819c8d"
wdt:P1417 "topic/determinant-mathematics"
wdt:P14534 "Matrix.det"
wdt:P1482 <https://cstheory.stackexchange.com/tags/determinant>
<https://math.stackexchange.com/tags/determinant>
<https://mathoverflow.net/tags/determinants>
<https://stackoverflow.com/tags/determinants>
wdt:P1568 set of complex n×n matrices
wdt:P1571 set of complex numbers
wdt:P18 <http://commons.wikimedia.org/wiki/Special:FilePath/Schema%20sarrus-regel.png>
wdt:P1851 set of complex n×n matrices
wdt:P227 "4138983-9"
wdt:P2347 "11285"
wdt:P244 "sh85037299"
wdt:P2534 "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>det</mi><mo>&#x2061;</mo><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mi>𝑨</mi></mrow><mo stretchy="false">)</mo><mo stretchy="false">=</mo><munder><mo stretchy="false">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x03C3;</mi><mo stretchy="false">&#x2208;</mo><msub><mi>S</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub></mrow></mrow></munder><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi data-mjx-texclass="OP" mathvariant="normal">sgn</mi><mo>&#x2061;</mo><mo stretchy="false">(</mo><mi>&#x03C3;</mi><mo stretchy="false">)</mo><mstyle displaystyle="true" scriptlevel="0"><munderover><mo stretchy="false">&#x220F;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo stretchy="false">=</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></munderover></mstyle><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo>,</mo><msub><mi>&#x03C3;</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></mrow></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
wdt:P2579 wd:Q114720351
linear algebra
wdt:P268 "11975737s"
wdt:P279 alternating multilinear map
similarity invariance
wdt:P2812 "Determinant"
wdt:P2924 "2691291"
wdt:P3365 "determinante"
wdt:P349 "00562696"
wdt:P3553 "19900291"
wdt:P373 "Determinant"
wdt:P3847 "determinants"
wdt:P4215 "determinant"
wdt:P4223 "determinanti"
wdt:P4342 "determinant"
wdt:P5008 Wikipedia:Vital articles/Level/4
wdt:P508 "32649"
wdt:P5610 "linalg1#determinant"
wdt:P6058 "divers/déterminant_dune_matrice_carrée_M_=_αij_dordre_n_sur_un_corps_K/42750"
wdt:P6104 WikiProject Mathematics
wdt:P6366 "158041659"
"2778383128"
wdt:P6385 "nauka_i_tehnika/matematika/OPREDELITEL.html"
wdt:P646 "/m/02c2w"
wdt:P6564 "expansion-of-determinants"
wdt:P691 "ph153485"
wdt:P7033 "scot/15495"
wdt:P7235 "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi data-mjx-texclass="OP" mathvariant="normal">sgn</mi><mo>&#x2061;</mo><mo stretchy="false">(</mo><mo stretchy="false">)</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>&#x03C3;</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>det</mi><mo>&#x2061;</mo><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mi>𝑨</mi></mrow><mo stretchy="false">)</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mo stretchy="false">&#x220F;</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mo stretchy="false">&#x2211;</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mi>𝑨</mi></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>S</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
wdt:P7305 "3999183"
wdt:P7554 "determinant"
wdt:P8189 "987007550422505171"
wdt:P8313 "determinant"
wdt:P8855 "102-06-20"
wdt:P910 Category:Determinants
wdt:P913 vertical bar brackets
wdt:P9621 "determinante"
wdt:P9941 "determinante"
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